The company acknowledged that it made a “mistake” approving the application, which depicts a crying baby and has users quiet the infant by vigorously shaking the smartphone. The quieted baby is shown with crosses on its eyes to indicate it’s dead.

Apple dropped the application from the App Store on Wednesday night following protests from child-abuse groups, including the National Center on Shaken Baby Syndrome and the Sarah Jane Brain Foundation, which said Thursday it plans to picket Apple Stores in 15 cities across the nation starting May 3.

“This app is deeply offensive and should not have been approved for distribution on the App Store,” an Apple spokeswoman told InformationWeek. “We sincerely apologize for this mistake.”

She declined to discuss whether the incident indicated that the company’s approval process was less than foolproof and in need of review. “We do have a process and this was a mistake,” she said. “I don’t have any comment beyond that.”

Apple’s refusal to disclose how the application found its way onto the App Store was one of several complaints the Sarah Jane Brain Foundation had with the company’s apology, which the group called “stale.”

“Who is this apology directed to?” said Patrick Donohue, founder of the foundation. “It’s directed at the media to kill the story. This is the most cynical apology I have ever seen.”

The group is calling on Apple to provide a full accounting on how the application was vetted and then launched on the App Store and who is being held accountable. In addition, the foundation wants Apple to devise a plan to “mitigate the harm they’ve now caused,” Donohue said.

The popularity of the App Store is evident in the 1 billion downloads reached Thursday in nine months. Many users of the online store and the iPhone are young men who as first-time fathers are often the ones who shake crying babies out frustration, causing severe brain damage or death, Donohue said. “You literally couldn’t have asked for a worse form of messaging for the demographic that are specifically targeted to prevent shaken baby syndrome.”

Violent shaking of an infant can cause pediatric traumatic brain injury, which is the leading cause of death and disability for children under 15 years old in the United States, according to the foundation. More than 5,000 deaths occur annually due to PTBI, and 17,000 children each year suffer permanent disability.

The group on May 3 plans to start a 15-day nationwide education tour for PTBI covering 15 cities. Donohue said the organization has added plans to hold protests in front of an Apple store in each city, unless it gets a satisfactory response from Apple. In addition, the foundation has sent letters to the boards of Apple andAT&T (NYSE: T), the exclusive iPhone seller in the United States, asking that they take action to meet the group’s demands.

A company called Sikalosoft developed Baby Shaker, which sold for 99 cents. The application is not the first controversial one connected to the App Store. In February, Apple rejected as “potentially offensive” an application that would have shown clips from South Park, the irreverent TV cartoon known for its scathing social commentary.